Can't texture paint in 3D or Image Editor with existing material nodes
I think that after looking at this, you can simplify your approach to a Color Mix node in front of the Principled Shader node to combine the texture paint and noise texture in ways you can't here with your set up. In the Color Mix node, you can actually choose from a drop down of multiple mix modes similar to a Photoshop layer blending mode like Add, Subtract, Mix(Normal), Multiply, etc.

If you have to use the two shader method because they are different materials, I woudl expect you would be mixing them with a stencil to make them show up in different parts - adding them together only cause them to wash out and is a waste of processing in the node tree using two Principled BSDF nodes like that.